Can't sleep, so thinking of physics. Yes, I'm weird.
Universe is flat because Relativity works. If universe weren't flat, relativity would not work. Relativity is based on the angles of a triangle adding up to exactly 180 degrees, you know. QED.
My model of how gravity, spacetime, and velocity work (see earlier posts) posits sine/cosine based laws of motion, energy, and perceived time. Redshift data proves this. Why does universal expansion appear to accelerate? Because the slopes of sin (x) and sin^2 (x) change. There is no actual acceleration or deceleration. It just appears that way. Because geometry says so.
The difference in energy levels (red shift) between two points is determined by the slopes of the individual energy curves. Everything has a energy-differential sphere around it. (Lowest energy in direction of motion, highest directly opposite, and neutral at 90 degrees to motion.) This is what causes motion, perceived time, and energy gain/loss (blue/red shift). The difference in slopes of any two objects determines this. This is also where you get sin^2 (x) from - you multiply the two together to find the total.
Or maybe I'm just stupid tired and getting everything wrong. That might very well be the case.